The sequence [2, 4, 6] is valid. Test other sequences to discover what makes a sequence valid. When you think you know, write down your guess, reveal the rule, and see how it compares.

(You should try to deduce the truth using as few tests as possible; however, your main priority is getting the rule right.)

You can play my implementation of the 2-4-6 problem here (should only take a few minutes). For those of you who already know the solution but still want to test your inductive reasoning skills, I've made some more problems which work the same way but apply different rules.

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I knew about 2-4-6 problem from HPMOR, I really like the opportunity to try it out myself. These are my results on the four other problems:


Number of guesses:

8 guesses of which 3 were valid and 5 non-valid


"A sequence of integers whose sum is non-negative"

Result: Failure


Number of guesses:

39 of which 23 were valid 16 non-valid


"Three ordered real numbers where the absolute difference between neighbouring numbers is decreasing."

Result: Success


Number of guesses:

21 of which 15 were valid and 6 non-valid


"Any three real numbers whose sum is less than 50."

Result: Success


Number of guesses:

16 of which 8 were valid and 8 non-valid


"First number is a real number and the other two are integers divisible by 5"

Result: Failure

Performance analysis

I'd say that the main failure modes were that I didn't do enough tests and I was a very bad number generator. For example, in indexD

I made 9 tests to test my final hypothesis 4 of which were valid, that my guess and the actual rule would give the same result for these 9 tests if I were actually good at randomizing is very small.

I could also say that I was a bit naive on the first test and that I'd grown overconfident after two successive successes for the final test.

Here is my playthrough with my though process:


>!0) [2, 4, 6] is VALID

>!Now I think, let's check if the rule is *2
>!1) [31, 62, 93] is VALID

>!Let's check if the rule is always true with 3 random numbers.
>!2) [6534525, 142536, 456342532] is NOT VALID

>!I wanted to check multiply by 3, but I repeated multiply by 2
>!3) [5, 10, 15] is VALID

>!Checking multiply by 3
>!4) [7, 21, 63] is VALID

>!Checking multiply by 10
>!5) [50, 500, 5000] is VALID

>!Now I am thinking: maybe any multiplication is ok? I cannot try them all, let's try constant addition:
>!6) [34, 35, 36] is VALID

>!Let's try constant subtraction
>!7) [5, 4, 3] is NOT VALID

>!Let's try increasing
>!8) [5, 64, 234] is VALID

>!Let's try increasing with random numbers
>!9) [12345, 123456, 1234567] is VALID

>!Let's try increasing or constant.
>!10) [5, 5, 6] is NOT VALID

>!Now I have made up my mind!

>!After 10 tests, your guess was . . .

>!"The sequence is valid if it is strictly increasing."


See FAQ for spoiler tags, it seems mods haven't seen your request.

I tried both and neither works

Hmm, yeah it's a bit hard to try stuff when there's no good preview. Usually I'd recommend rot13 chiffer if all else fails but for number sequences that makes less sense.

Hey, it seems the app is getting its own rule wrong. :)

It says "Three numbers in ascending order"; however [0;0;0] is accepted as valid. It should say "in non-descending order".

[ADDED] Also indexA

shows the rule "Two odd numbers, one even; any order" but does not accept [-1, -2, -3].

Well, that's embarrassing. Fixed now; thank you.

I got 1 right, 1 partially right, and 2 I couldn't figure out and gave up.

Have you played the game Understand?